Question

Create an exponential growth function, f(x), to model a population of frogs that is growing every year. Identify the principal amount, the growth rate, and the appropriate domain and range for your function. Explain how these key features would affect the graph of f(x).

Answer 1

f(x) = A * (B)^(x)
x is time in years
A is initial frog population at time x = 0 (the reference year where the model begins)
If B > 1 it will be exponential growth. If B < 1 it will be exponential decay.
The growth rate is how much B is over 1. That is (B-1) is the growth rate.

Answer 2

Domain: x >= 0 or [0, infinity)
Range: [A, infinity)

A is where the graph touches (or intersects) the y axis.
If B is large, f(x) will rise steeply.
If B is just a little over 1, say 1.001, then f(x) will rise a little slower (still exponential growth) but the curve will be broader.

Answer 3

Thank you so much!

Answer 4

Is that all?

Answer 5

yep. you are welcome.